If P is a point (x,y) on the line y=ā3x, such that P and the point (3,4) are on the opposite sides of the line 3xā4y=8, then
A
x>815
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B
x>85
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C
y<−85
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D
y<−815
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Solution
The correct options are Cx>815 Dy<−85 Let L=3x−4y−8=0 be the equation of line and P(x,y) and Q(3,4) are given points. Then P and Q are on opposite side of the line iff L11L22<0 P is a point on the line y=−3x. i.e P=(x,−3x) ∴L11L22=15x−8−15<0 ⇒x>815 ⇒y=−3x<−85 Hence, options A and C.